new aerosol models for the retrieval of aerosol optical ...from the seawifs and modis sensors over...

New aerosol models for the retrieval of aerosol opticalthickness and normalized water-leaving radiances

from the SeaWiFS and MODIS sensors overcoastal regions and open oceans

Ziauddin Ahmad,1,2,* Bryan A. Franz,1 Charles R. McClain,1 Ewa J. Kwiatkowska,1,3

Jeremy Werdell,1,4 Eric P. Shettle,5 and Brent N. Holben1

1NASA Goddard Space Flight Center, Greenbelt Road, Greenbelt, Maryland 20771, USA2Science and Data Systems, Inc., 16509 Copperstrip Lane, Silver Spring, Maryland 20906, USA

3Science Applications International Corporation, 10260 Campus Point Drive, San Diego, California, 92121, USA4Science Systems and Application, Inc., 10210 Greenbelt Road, Lanham Maryland 20706, USA

5Naval Research Laboratory, Washington, D.C. 20375, USA

*Corresponding author: [email protected]

Received 18 February 2010; revised 20 July 2010; accepted 26 August 2010;posted 7 September 2010 (Doc. ID 124415); published 5 October 2010

We describe the development of a new suite of aerosol models for the retrieval of atmospheric and oceanicoptical properties from the SeaWiFS and MODIS sensors, including aerosol optical thickness (τ),angstrom coefficient (α), and water-leaving radiance (Lw). The new aerosol models are derived from Aero-sol Robotic Network (AERONET) observations and have bimodal lognormal distributions that are nar-rower than previous models used by the Ocean Biology Processing Group. We analyzed AERONET dataover open ocean and coastal regions and found that the seasonal variability in the modal radii, parti-cularly in the coastal region, was related to the relative humidity. These findings were incorporated intothe models by making the modal radii, as well as the refractive indices, explicitly dependent on relativehumidity. From these findings, we constructed a new suite of aerosol models. We considered eight relativehumidity values (30%, 50%, 70%, 75%, 80%, 85%, 90%, and 95%) and, for each relative humidity value, weconstructed ten distributions by varying the fine-mode fraction from zero to 1. In all, 80 distributions(8Rh × 10 fine-mode fractions) were created to process the satellite data. We also assumed that thecoarse-mode particles were nonabsorbing (sea salt) and that all observed absorptions were entirelydue to fine-mode particles. The composition of the fine mode was varied to ensure that the new modelsexhibited the same spectral dependence of single scattering albedo as observed in the AERONET data.The reprocessing of the SeaWiFS data show that, over deep ocean, the average τ865 values retrieved fromthe new aerosol models was 0:100� 0:004, which was closer to the average AERONET value of 0:086�0:066 for τ870 for the eight open-ocean sites used in this study. The average τ865 value from the old modelswas 0:131� 0:005. The comparison of monthly mean aerosol optical thickness retrieved from the Sea-WiFS sensor with AERONET data over Bermuda andWallops Island show very good agreement with oneanother. In fact, 81% of the data points over Bermuda and 78% of the data points over Wallops Island fallwithin an uncertainty of �0:02 in optical thickness. As a part of the reprocessing effort of theSeaWiFS data, we also revised the vicarious calibration gain factors, which resulted in significantimprovement in angstrom coefficient (α) retrievals. The average value of α from the new models overBermuda is 0:841� 0:171, which is in good agreement with the AERONET value of 0:891� 0:211.The average value of α retrieved using old models is 0:394� 0:087, which is significantly lower thanthe AERONET value. © 2010 Optical Society of AmericaOCIS codes: 070.4550, 070.6110, 120.5050, 120.6650.

0003-6935/10/295545-16$15.00/0© 2010 Optical Society of America

10 October 2010 / Vol. 49, No. 29 / APPLIED OPTICS 5545

1. Introduction

One of the most challenging tasks in satellite remotesensing of the oceans is to accurately quantify thephytoplankton abundance, colored dissolved organicmatter (CDOM), and inherent optical properties ofthe water column. These quantities are determinedfrom the spectral distribution of water-leaving ra-diances (Lw) at the ocean surface, which are only asmall fraction of the downwelling solar irradiancethat is backscattered to the top of the atmosphere(TOA) by subsurface constituents of the ocean. Underideal conditions of clear water in the deep ocean(depth > 1000m), Lw in the blue part of the spectrumis only about 10%–15% of the total radiance at theTOA, which is mostly dominated by Rayleigh andMie scattering by air molecules and aerosols, respec-tively, in the atmosphere. In coastal areas like Che-sapeake Bay, the contribution of Lw to TOA radiancemay decrease to less than 5% due to an increase inabsorption by chlorophyll and CDOM in the watercolumn. Hence, to accurately retrieve the water-leaving radiance and derive bio-optical propertiesof the ocean from satellite remote sensing data, anaccurate determination of the atmospheric contribu-tion to TOA radiance, also known as atmosphericcorrection, is required.

Although the physics of the scattering by air mo-lecules and aerosols is well understood, the accuracyof atmospheric correction is dependent on the deter-mination of microphysical and optical properties(e.g., size distribution and complex index of refrac-tion) of aerosols that, unfortunately, are temporallyand spatially variant in concentration and particletype. The different types of atmospheric aerosols ob-served over oceans and their origins are discussed inthe review article by Husar et al. [1] and referencestherein. They are briefly summarized as follows.Over open oceans, where maritime influencesdominate, aerosols are generally nonabsorbing andmainly consist of sea salt and water produced fromthe breakup of water bubbles. In addition to thesenaturally occurring aerosols, there are anthropo-genic aerosols, such as sulfates produced by indus-tries and transported across the North Atlanticand North Pacific Oceans. Similarly, there are smokeaerosols that are produced from biomass burning inWestern Africa and Central America. Sulfate aero-sols are nonabsorbing, whereas smoke shows strongabsorption, particularly in the red part of the spec-trum. Another strongly absorbing aerosol found overthe Atlantic Ocean is Saharan dust, which originatesfrom Western Africa and is transported across theCentral Atlantic to North and Central America.Likewise, aerosols originating from the Gobi desertcross the Western Pacific Ocean and are often ob-served over the continental United States of Ameri-ca. Both the Saharan and Gobi dust aerosols aremore absorbing in the blue than in the red part ofthe spectrum.

Aerosols are often classified into groups based ontheir origin. For example, Shettle and Fenn [2] (here-

after SF79) broadly divide the aerosols into two maingroups: continental and maritime aerosols, andfurther subdivide the continental aerosols into ruraland urban origins andmaritime aerosols into oceanicand continental origins. d’Almeida et al. [3] provide amore comprehensive classification of aerosols for thepurpose of climate studies. In particular, they dividemaritime aerosols into three subcategories: cleanmaritime, maritime mineral, and maritime polluted.They define the clean-maritime aerosols as consistingof sea salt and non-sea-salt-sulfate (NSS) aerosolsfound in remote areas of oceans, maritime-mineralaerosols as consisting of desert dust and aerosols ofmaritime origin, and maritime-polluted aerosols asconsisting of crustal, anthropogenic aerosols trans-ported through continental air mass and aerosols ofmaritime in origin.

Over the past several decades, many attemptshave been made to describe the size distribution ofaerosols through analytical functions. Based on fieldmeasurements, Junge [4] proposed a power-law func-tion, and Deirmendjian [5,6] suggested use of a mod-ified gamma function to describe the size distributionof aerosols. Deirmendjian also showed that the mod-ified gamma function correctly describes the polari-zation properties of aerosols and water clouds. Later,Davies [7] reported that Junge’s power law does notaccurately account for large particles in observed sizedistributions, and proposed a lognormal function todescribe the size distribution of aerosols. Based onhis work, it is now customary to assume lognormaldistribution for aerosol size distribution. Also, com-pared to Deirmendjian’s modified gamma distribu-tion, the constants of the lognormal distribution aremore intuitive. Another interesting feature of thelognormal distribution is that each component ofthe distribution has a unique modal radius, standarddeviation, and refractive index, and can be traced toits source or origin. In their classification of aerosols,both SF79 and d’Almeida et al. [3] assumed lognor-mal distributions to describe the aerosols in theatmosphere.

To process large amounts of satellite data from sen-sors like SeaWiFS, Gordon and Wang [8] (hereafterGW94), andGordon [9] used SF 79 ’s lognormal distri-butions of tropospheric and maritime aerosols andproposed a suite of aerosol models to estimate atmo-spheric correction. They constructed these distribu-tions to represent tropospheric, coastal, maritime,and oceanic aerosols. Their tropospheric and oceanicmodels were identical to SF79 ’s lognormalmodels fortropospheric and maritime aerosols, whereas theirmaritime and coastal aerosol models were bi-modallognormal models constructed by combining 99%(99.5%) of SF79 tropospheric and 1% (0.5%) of mari-time aerosols, by number of particles, respectively.It should be noted that these aerosol models do notrepresent smoke or Saharan dust over the ocean. An-toine and Morel [10] used similar aerosol models toprocess MERIS data; however, their suite of opera-tional models also includes dust models. They refer

5546 APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010

to their models as marine, urban, continental, anddust aerosolsmodels.The former twoarederived fromSF79 ’s models, and the latter two are taken fromWorld Climate Radiation Program [11], and frommeasurements reported by Schütz [12]. Both GW94and Antoine and Morel account for the effect of rela-tive humidity on the aerosols’microphysical and opti-cal properties. They use the variation of the meangeometric radius and refractive index of aerosols withrelative humidity from SF79, which was based on thedata of Hänel [13].

With development of the AERONET program byNASA in the late 1990s, a large database of sunphot-ometer derived aerosol properties, including opticalthickness and size distributions over land and oceanicsites, are now available to investigators for scientificresearch. Using AERONET data, Smirnov et al. [14]reported aerosol size distributions over open oceansthat are quite different from GW94 ’s maritime aero-sol models. For example, GW94 ’s maritime aerosolmodel for relative humidity of 90% has modal radii(standard deviation) values for fine and coarse modesin volume size distribution space as 0.274 (0.806) and4.842 ð0:921Þ μm, respectively; whereas, Smirnov’saverage values for fine and coarse modes for theLanai, Nauru, and Tahiti sites in the Pacific Oceanfrom the most recent processing of the AERONETdata are 0.177 (0.477) and 2.555 (0.678), respectively.If we add two other sites in Smirnov’s paper, namely,Bermuda and Ascension Island, then the average va-lues for the fine and coarse modes become 0.171(0.460) and 2.503 (0.676), respectively. In otherwords,AERONET aerosol size distributions derived frommaritime locations are narrower than GW94 ’s.

A few years ago, Wang et al. [15] analyzed the Sea-WiFS derived atmospheric and oceanic data productsproduced by the Ocean Biology Processing Group(OBPG) and concluded that, although, the water-leaving radiances were in good agreement with thein situmeasurements, the retrieved aerosol products(optical thickness and angstrom coefficient) differedsignificantly from the AERONET measurements.They also reported that GW94 ’s models often over-estimate atmospheric correction in the coastal re-gion, particularly over the Eastern U.S., where thewater-leaving radiance retrieval in the blue channel(412nm) of the SeaWiFS and MODIS sensors issometimes negative.

In this paper, we describe the details of an effort todevelop a new set of aerosol models to improve thequality of the atmospheric correction and retrievedaerosol properties from SeaWiFS and MODIS sen-sors. These models are designed to span the rangeof aerosol size distributions and optical propertiesobserved at maritime AERONET sites, includingboth open-ocean and coastal environments. For infor-mation on the open ocean, we focus on a suite ofAERONET sites located on small islands away frommajor land masses. For the coastal environment, theChesapeake Bay Region (CBR) serves as a usefulproxy, as it spans a wide range of water types from

highly turbid in the northern extent to nearly oceanicin the south, with aerosol influences from industrialcities, suburban areas, agricultural land use, and theAtlantic Ocean. The CBR is also well equipped withthree long-standing AERONET stations and an on-going water-quality monitoring program.

We incorporate the models developed from theseAERONET observations into the global processingchain within the OBPG, and show how they signifi-cantly improve the agreement of retrieved aerosolproperties from SeaWiFS relative to in situmeasure-ments. We also explore the impact of this improvedaerosol retrieval on the quality of atmospheric cor-rection and water-leaving radiance retrievals. Theaerosol models developed through this work will ul-timately be applied to the reproduction of all opera-tional ocean color products distributed by NASAfrom the SeaWiFS and MODIS sensors. This is thefirst effort to update the operational aerosol modelssince the original atmospheric correction approachfor SeaWiFS was developed by GW94 in the early1990s.

2. AERONET Data

A. Background

The details of AERONET network and measure-ments are described in many papers, includingHolben et al. [16,17], Dubovik and King [18], Duboviket al. [19–22] and Sinyuk et al. [23]. Briefly,AERONET data consist of optical thickness and mi-crophysical parameters of aerosols in the atmo-sphere. The optical thickness is derived from thedirect measurements of the Sun in eight spectralbands centered at 340, 380, 440, 500, 670, 940, and1020nm, and microphysical properties, such as aero-sol size distribution, are derived from diffuse sky ra-diance measurements, generally in four bands at440, 670, 870, and 1020nm along the principal planeand along the solar almucantar. The principal planemeasurements are carried out by varying the zenithangle at a fixed azimuth angle and the solar almu-cantar by varying the azimuth angle at a constantzenith angle. The aerosol optical thickness is derivedfrom the Beer–Bouguer law, where the contributionsfrom Rayleigh and trace gas optical thicknesses aresubtracted from the total optical thickness derivedfrom the slope of the log of irradiance versus pathlength line. The volume size distribution (ðdV=dðln rÞÞ is retrieved in 22 equidistance bins in ln rspace, where the radius of the particle, r, varies from0.05 to 15 μm.

A detailed analysis of the AERONET retrievedaerosol volume size distributions shows that thedistributions can be approximated by a sum of twolognormal distributions written as

dVðrÞd ln r

¼X2i¼1

Voiffiffiffiffiffiffi2π

pσiexp

�−

�ln r − ln rvoiffiffiffi

2p

σi

�2�; ð1Þ

where Voi is the volume of the particles, rvoi is thevolume geometric mean radius, and σi is the


geometric standard deviation. The subscript i repre-sents the ith mode of the distribution.

In the number density space, Eq. (1) takes the form

dNðrÞd ln r

¼X2i¼1

Noiffiffiffiffiffiffi2π

pσiexp

�−

�ln r − ln rnoiffiffiffi

2p

σi

�2�; ð2Þ

where Noi is the number of particles, and rnoi is themean geometric radius of the ith distribution, andthe radius rnoi and Noi are, respectively, related torvoi and Voi as

ln rnoi ¼ ln rvoi − 3σ2i ; ð3aÞ

Noi ¼ Voi½0:75=ðπr3noiÞ� expð−4:5σ2i Þ: ð3bÞ

Two other quantities of interest are effective radius(reff ) and effective variance (veff ), which are definedas

reff ¼Zrmax

rmin

πr3nðrÞdr=Zrmax

rmin

πr2nðrÞdr; ð4aÞ

veff ¼Zrmax

rmin

ðr − reff Þ2πr2nðrÞdr=r2effZrmax

rmin

πr2nðrÞdr; ð4bÞ

where

nðrÞ ¼ dN=dr:

Hansen and Travis [24] have shown that all distribu-tions (for example, modified gamma, power law, andvarious lognormal distributions) that have the samevalues of reff and veff have very similar scatteringproperties. We use these parameters, particularly ef-fective radius, in discussing the properties of theopen-ocean and regional aerosol models describedin the following sections.

B. Aerosol Properties Over Open Oceans and CoastalRegions

1. Size Distribution

To understand the characteristics of aerosols overopen oceans, we searched the AERONET databaseand identified 15 sites for the analysis. On furtherexamination we found that many of those siteshad limited data records. We selected eight sites thathad about 150 or more daily averaged observations.These sites, along with their latitude–longitude anddata span, are listed in Table 1 and shown in Fig. 1.Three of these sites (Lanai, Midway, and Tahiti) arein the Pacific Ocean, three (Cape Verde, AscensionIsland, and Bermuda) are in the Atlantic Ocean,and the final two (Kaashidhoo and Darwin) are inthe Indian Ocean. Although Darwin is a coastal site,here we have treated it as an open-ocean site. It isrecognized that some of these sites, such as CapeVerde, may have episodic influx of desert dust or bio-mass burning aerosols in addition to oceanic aero-sols, but the retrievals need to work for those cases,also. We also selected three sites (SERC, WallopsIsland, and COVE) over the CBR. These sites coverthe upper, middle, and lower regions of ChesapeakeBay. Details of these sites are also listed in Table 1.Also, to ensure compatibility with the operationalprocessing of the satellite data fromMODIS and Sea-WiFS sensors, where scenes with optical thicknessgreater than approximately 0.3 are generallymasked as clouds, we selected only those measure-ments where retrieved aerosol optical thickness wasless than or equal to 0.3. Finally, to get a better un-derstanding of the aerosol microphysical and opticalproperties, we converted the daily averaged data intomonthly averaged data and examined in detail theseasonal behavior of a few selected parameters,including mean geometric modal radius [in dV=dðln rÞ space], standard deviations, effective radius,and relative concentration of fine- and coarse-modeparticles. We found that, over the open ocean, themonthly mean data of modal radii showed largevariations; however, when we constructed themonthly climatology, the large variations disap-

Table 1. Name and Location of the AERONET Sites and Number of Observations (Daily Averaged) Used for Analysis of Aerosol SizeDistribution over Chesapeake Bay and Open Ocean

Type Site Location (Lat., Long.) Data Record No. of Observations

Coastal COVE 36.90N, 75.710W Oct. 1999–Dec. 2006 740Wallops Island 37.942N, 75.475W Jul. 1993–Aug. 2007 985SERC 38.883N, 76.500W Nov. 1994–Jun. 2006 468

Open ocean Lanai 20.735N, 156.922W Nov. 1996–Oct. 2004 678Cape Verde 16.733N, 022.935W Jan. 1996–Apr. 2007 512Tahiti 17.577S,149.606W Aug. 1999–Oct 2003 247Kaashidhoo 04.965N, 073.466E Feb. 1998–May 2000 149Darwin 12.424S, 130.892E Apr. 2004–Nov. 2005 235Ascension Island 07.976S, 014.415W Dec. 1998–May 2006 293Bermuda 32.370N, 064.696W Apr. 1996–Nov. 2002 192Midway Island 28.210N, 177.378W Jan. 2001–Sep. 2006 237


peared and there was a relatively smooth variationin the modal radii values with season. Over theCBR, the three sites had very similar variation withseason, suggesting that aerosol characteristics overthe upper, middle, and lower bay were consistent.Figures 2(a)–2(c) show the monthly climatology of

the mean geometric radius and standard deviationof the fine and coarse modes for both the open-oceanand CBR aerosols. For open ocean, the fine-mode ra-dius monotonically decreases from January to June,shows a bump in the months of July and August, andthen increases monotonically from September untilDecember. The maximum value (0.177) occurs inJanuary and the minimum value (0.162) in May,as well as in June.We do not find any discernible sea-sonal trend in the coarse-mode values. The maxi-mum value (2:564 μm) occurs in December and theminimum value (2:279 μm) in April. Similarly, thereis no trend in the standard deviation values of thefine and coarse modes over the open ocean. The max-imum value of the standard deviation, 0.485 (0.676),for the fine (coarse) mode occurs in April (March),while the minimum values of 0.453 and 0.656,respectively, for the fine and coarse modes occur inDecember. For the CBR aerosols, we find that thefine-mode radius is smaller in the months of Apriland October (∼0:16 μm) than in July and August

Fig. 1. Locations of oceanic and coastal AERONET sites used inthe present study.

Fig. 2. (a) Monthly mean geometric radius of fine-mode aerosols (in volume distribution space) observed over open ocean and CBR. (b)Same as in (a), but for coarse-mode aerosols. (c) Monthly mean standard deviation of fine- and coarse-mode aerosols over open ocean andthe CBR. (d) Monthly mean fraction (by volume) of the fine-mode distributions over open ocean and the CBR. (e) Effective radius ofaerosols over open ocean and the CBR.


(∼0:185 μm). The coarse-mode radius shows a mini-mum value (2:3 μm) in the month of April and max-imum value (3:2 μm) in June, July, and August.Unlike the fine mode, the coarse mode does not showany minimum in September, but it slowly decreasesto 2:9 μm in December. With respect to standard de-viation, we find that, for the fine mode, the values areslightly greater in January and February (∼0:46)than in June and October (∼0:42); whereas, for thecoarse mode, the standard deviation value is maxi-mum (0.7) in the month of April and minimum(∼0:615) in the months of August and September.

We also examined the fine-mode fraction [Fig. 2(d)]and found no seasonal trend over the open ocean. Themaximum and minimum values were, respectively,0.245 and 0.182, and occurred in September and July.The average value of the fine-mode fraction was0.212. Over the CBR, we do find a trend in the fine-mode-fraction values. It is significantly higher dur-ing the months of June, July, and August (0.729,0.754, and 0.759) than for other months, for whichthe value varies from 0.490 in April to 0.658 inSeptember. The average value of the fine-mode frac-tion over the CBR is 0.632.

The effective radius shows a weak trend with sea-son [Fig. 2(e)]. Over open ocean, it decreases mono-tonically from January (0:680 μm) to May (0:571 μm),shows a sudden increase during the months of Juneand July (0:648 μm and 0:664 μm), and then reachesanother minimum (0:613 μm) in September. Finally,it slowly reaches to its maximum value (0:714 μm) inDecember. The average value of the effective radiusover open ocean is 0:638 μm. Over the ChesapeakeBay, the trend is very weak. It varies from 0:279 μmin January to 0:309 μm in April, and then drops to0:234 μm in June. Afterward, it fluctuates between0:280 μm in September and 0:237 μm in December.We find the average value of the effective radius overthe CBR to be 0:265 μm, indicating the strong influ-ence of the fine-mode tropospheric aerosols. A sum-mary of the average values of the parametersdescribed above is given in Table 2.

2. Single Scattering Albedo

An examination of the single scattering albedo (SSA)data over the open ocean shows that, most of thetime, the AERONET stations did not report theSSA values. For the eight open-ocean sites, 97.1%of the data (2469 daily averaged observations) did

not have any SSA values. We believe that this ismostly due to large uncertainty in the retrievedSSA values when the aerosol optical thicknessesare small (<∼ 0:2), which is generally the case overopen ocean. For the remaining 2.9% of the data (74daily averaged observations), which came from foursites: Cape Verde, Kaashidhoo, Darwin, and Ascen-sion Island, the average value SSA for the 440nmband was 0:872� 0:051. These cases included a sig-nificant contribution from dust and/or biomass burn-ing aerosols, in addition to the normal oceanicaerosols.

Over the CBR, 19.3% of the data (423 daily aver-aged observations) did not have any SSA value, andonly 5% (110 observations) of the reported data hadSSA (440nm) values of less than 0.935. The frequencydistribution [see Fig. 3(a)] shows a peak around 0.97.Since AERONET assigns a low confidence level toSSA values when aerosol optical thickness at870nm (τ870) is small (less than 0.2), we selected datawhere τ870 fell between 0.2 and 0.3 to get a better un-derstanding of SSA values over the CBR. We foundthat, for the dataset where 0:2 ≤ τ870 ≤ 0:3 and SSA ≥

0:935, the SSAwas essentially constant (0.975) over asix month period from May to October [Fig. 3(b)]. Inour dataset, we did not find observations for wintermonths that would satisfy the optical thickness andSSA criteria stated above. Another quantity of inter-est was the spectral dependence of the SSA. Saharandust aerosols have a positive slope in the visible partof the spectrum, whereas maritime-polluted aerosolsexhibit negative slope (Dubovik et al. [20]). To exam-ine the spectral slope of the SSA in our data, we de-termined the mean value for each wavelength ofthe AERONET observations. The result of this exer-cise is shown inFig. 3(c),wherewe find a linear depen-dence of SSA on wavelength. Here, slope is negative,that is, SSA decreases with an increase in wave-length, indicating that CBR aerosols can be classifiedas maritime-polluted aerosols. For the open-oceandata, we found only eight observations that would sa-tisfy the optical thickness criteria (0:2 ≤ τ870 ≤ 0:3)and all of them had SSAð440nmÞ ≤ 0:935. It appearsthat most of the absorbing aerosol data over the openocean were due to smoke and soot, at the four islandstations.

While analyzing the data over the CBR and openocean, we found a linear relationship between theaerosol angstrom coefficient (α440), which definesthe spectral dependence between τ440 and τ865, and

Table 2. Average Values of Modal Radii ðrvf ; rvc Þ, Standard Deviations ðσf ; σc Þ, Effective Radius reff, and Fine-Mode Fraction f for Fine- andCoarse-Mode Aerosols over Open Ocean and Chesapeake Baya

Fine Mode Coarse Mode

rvf σf f rvc σc 1 − f reff NOpen ocean 0.171 0.462 0.257 2.492 0.678 0.743 0.612 1794Chesapeake Bay 0.168 0.427 0.629 2.790 0.664 0.371 0.266 2193

aThe subscripts v, f , and c, respectively, refer to volume space, fine mode, and coarse mode of the aerosols, andN in the last column of thetable represents the total number of daily averaged observations. (Note: these numbers slightly differ from mean of the monthly averagevalues).


fine-mode fraction that satisfies both the CBR andopen-ocean aerosols. This is shown in Fig. 3(d).The correlation between these quantities is easily ex-plained by the fact that the angstrom coefficient islarge when the effective radius of aerosols is smalland it decreases as the effective radius of the aerosolsincreases, while the fine-mode-fraction value is largewhen the effective radius is small and vice versa. Wedid not expect, however, that this relationship be-tween angstrom coefficient and fine-mode fractionwould be linear.

3. Aerosol Models for Satellite Data Reduction

A. Size Distributions

In the past, many authors, including Tanre et al. [25],Omar et al. [26], Gross et al. [27], and Zagolski et al.[28] have used AERONET data to develop models toretrieve microphysical and optical properties of aero-sols from satellite observations. For example, Tanreet al. [25] used AERONET data and constructed fivemodels of fine-mode and four models of coarse-modeaerosols, and then used the 20 combinations of thefine and coarse modes to retrieve aerosol propertiesover the ocean from observations taken by MODISsensors. Omar et al. [26] used cluster analysis tech-niques to classify all available AERONET data overland and ocean into six categories: desert dust, bio-mass burning, background rural, polluted continen-tal, marine, and dirty pollution. These six categoriesare being used to retrieve aerosol properties from theCALIPSO data. Unfortunately, their method yieldsonly one aerosol model for all maritime conditions.

Gross et al. [27] used a neural network techniqueto classify the AERONET data into 64 models. How-ever, they recommend only eight models to processocean color data from SeaWiFS. Most recently,Zagolski et al. [28] proposed an AERONET-basedclimatology of aerosol models to retrieve oceanicparameters such as chlorophyll concentration andprimary productivity. However, they do not suggestany method to account for the seasonal variationsin the modal radii of the aerosol distributions, parti-cularly in the coastal regions, such as CBR, as shownin Figs. 2(a) and 2(b).

Below, we describe the details of our new aerosolmodels to retrieve oceanic parameters, such as chlor-ophyll concentration and primary productivity, fromSeaWiFS and MODIS sensors. Based on the resultspresented in the preceding section, it seems logicalto develop sets of aerosol models where themicrophy-sical and optical properties are simply the monthlymeanvalues of theAERONETdata, but this approachis problematic. First, wedo not haveSSAalbedo valuefor the months of January, February, March, April,November, and December [see Fig. 2(b)]. In addition,although such a suite of models will, on the average,produce reasonable retrievals, the individual retrie-valswill have large errorsbecause the relativehumid-ity (Rh) varies from day to day and often shows largevariation. Using data from the National Climate En-vironment Predictions (NCEP), we find that Rh overthe CBR generally varies from 70% to 80% but, often-times, it drops to almost 40%. On the West Coast ofCalifornia, the Rh often drops to 25%–30%. Overthe open ocean, the relative humidity generally varies

Fig. 3. (a) Frequency distribution of SSA at 440nm using all observations in the combined dataset of SERC, Wallops Island, and COVEsites. Only 5% of the data have SSA ≤ 0:935. (b) Monthly mean value of SSA (ωo) of all observation, where 0:2 ≤ τ870 ≤ 0:3. The dataset didnot have observations for the month of January, February, March, April, November, or December that satisfied the above stated opticalthickness criteria. (c) Spectral dependence of SSA (ωo) of all CBR data where 0:2 ≤ τ870 ≤ 0:3 and ωo ≤ 0:935. (d) Relationship betweenangstrom coefficient (α440) and fraction of fine-mode aerosols.


from75%to85%, but it oftendrops to 65%or increasesto90%.Hänel [13] andSF79have shown that the radiiof the particles both in the fine and coarse mode in-crease with relative humidity. In general, the rateof increase is larger forRh > 70%andbecomes almostexponential beyondRh > 95% (Hänel [13], Wang andMartin [29]). Furthermore, with an increase in rela-tive humidity, the effective value of the refractive in-dex (both real and imaginary) approaches that ofwater, which is nonabsorbing. Another issue is thatthe AERONET retrieval algorithm assigns the samevalue of refractive index (or SSA) to both the fine- andthe coarse-mode particles. We believe this is not cor-rect because, over the open ocean and away fromthe polluted areas, the coarsemode primarily consistsof sea salt,which isnotabsorbing. Ifweaccept that thecoarse-mode particles are mostly sea-salt particles,then we must change the refractive index of thefine-mode particles to get the same retrieved SSA.

To develop models of aerosols for coastal and open-ocean conditions, we assumed that the aerosols couldbe represented by a sum of two lognormal distribu-tions, one representing the fine mode and the otherrepresenting the coarse mode. We further assumedthat the fine-mode aerosols are continental in natureand the coarse-mode aerosols are oceanic in nature.This means that coarse-mode aerosols are nonab-sorbing and all absorption is due to fine-mode parti-cles. We do recognize that, over the open ocean, thefine-mode aerosols will contain significant amountsof non-sea-salt sulfate aerosols, which are nonab-sorbing. However, over the open ocean, the fractionof fine-mode aerosol is small (∼20%) and the coarsemode (∼80%) dominates the scattering process. Itshould be noted that these fractions are by volumeand not by the number of aerosol particles, as wasthe case for the GW94 ’s ocean and coastal modelsdiscussed in Section 1. The exact percentages willvary with Rh, since the coarse-mode sea-salt parti-cles will grow more with increasing Rh than willthe continental origin, fine-mode particles.

To incorporate the effect of relative humidity onthe growth of fine- and coarse-mode aerosols, we fol-lowed a method first proposed by Hänel [13] and la-ter used by SF79 to determine the effective refractiveindex (m), and modal radii (rf and rc) at a number ofRh values from 30% to 95%. Hänel’s method involvesdetermining the radius as a function of relative Rhfrom the wet-to-dry mass ratio, which is given bythe following expression (Hänel [13]):

rðawÞ ¼ ro

�1þ ρmwðawÞ

mo

�3; ð5Þ

where aw, called water activity, is the same asRh cor-rected for the curvature of the particle surface, ro isthe radius of the particle forRh ¼ 0,mo is the mass ofthe dry particle, mw is the mass with condensedwater, and ρ is the ratio of wet-to-dry mass densityof aerosols. Hänel [13] also provided tabular valuesfor the ratios mw=mo and ρ for six types of aerosols

for a number of Rh values varying from 20% to99%. In this paper, we have assumed that the growthrates of our fine- and coarse-mode aerosols, respec-tively, are the same as Hänel’s tropospheric and mar-itime aerosols.

Because the AERONET data do not report the Rhvalues at the observation sites, we assumed that themonthly average values of modal radii for the fineand coarse modes correspond to the climatologicalvalues of Rh over each site, as determined fromNCEP monthly climatologies. This allowed us to de-termine a dry-mass radius value for every monthlyaverage value of the modal radius. We averagedthe dry-mass radius values for the fine and coarsemodes and then determined rðRhÞ for a number ofRh values from 30% to 99% using Hänel’s tabulatedvalues for ρ and mw=mo for tropospheric and mari-time aerosols. The results on the variation of modalradius and standard deviation with Rh for openocean and CBR are shown in Figs. 4(a)–4(d).

For the modal radius, the agreement between thedata and the model results is good, except for coarsemode over open ocean, where, forRh < 75%, the mod-el values are lower than the data. The reverse is seenfor Rh > 80%. For the standard deviation, the rela-tionship is very noisy. We do not have any modelto relate the standard deviation with Rh, and theleast square lines in Figs. 4(c) and 4(d) show weaktrends that we find difficult to interpret. We, there-fore, used the average value to represent thestandard deviation, which essentially makes itindependent of Rh.

B. Optical Properties (Refractive Index and SingleScattering Albedo)

The next task in developing the models was to deter-mine the index of refraction such that the predictedvalue of SSA agrees with observed value and showssimilar spectral dependence. Initially we assumedthat our fine- and coarse-mode aerosols are the sameas SF79 ’s tropospheric andmaritime aerosol models.They define their tropospheric aerosols as consistingof a mixture of water-soluble substances, such as am-monium and calcium sulfate (70%), and dustlikeaerosols (30%), and maritime aerosols as consistingof sea salts. We used SF79 ’s dry-mass refractive in-dex values and, using the following equation (Hänel[13]), computed the refractive index values for anumber of Rh values from 30% to 95%. The numer-ical values are reported at the nominal center wave-lengths of the SeaWiFS sensor given in Table 3:

n ¼ nw þ ðno − nwÞ�rorrh

�3; ð6Þ

Here, the symbols nw and no, respectively, refer to thecomplex indices of refraction of water and dry aero-sols, and ro and rrh, respectively, refer to the radius ofthe aerosols in the dry state and at Rh.

To summarize, based on AERONET observations,we constructed bimodal lognormal aerosol size


distributions, where the modal radii and refractiveindex values were explicitly dependent on Rh. Forthe purposes of generating lookup tables (LUTs),we considered eight values of Rh (30%, 50%, 70%,75%, 80%, 85%, 90%, and 95%). We did not considerRh values greater than 95% because, as stated ear-lier, the modal radius values for both the fine- andthe coarse-mode radii increase almost exponentiallybeyond Rh > 95%. The tabular values of the modalradius, standard deviation, and the ratio of thewet-to-dry radius for the fine- and coarse-mode aero-sols are given in Table 4. For standard deviation ofthe bimodal distributions, we used the average valueof the monthly means reported in Figs. 4(c) and 4(d).The rationale was that, although there were trendsin the data, there was no guiding physics to extendthe trend outside the humidity range of the observa-tions. The refractive index values were determinedfrom Eq. (6) using tabular data in Table 3 for Rh ¼0 and the wet-to-dry radius ratio given in Table 4.

After selecting the values of modal radii, standarddeviations, and refractive indices of the fine and

coarse modes for each humidity value, we con-structed ten distributions by varying the fine-modefraction from zero to 1. In other words, we created80 distributions to process the satellite data. In thispaper, the ten aerosol distributions are referred asMnn, where nn represents the aerosol size distribu-tion number. Examples of two such distributions forRh ¼ 50% and Rh ¼ 80% are shown in Fig. 5(a). Forcomparison purposes, we also show, in Fig. 5(b),GW94 ’s [8] coastal and maritime aerosol size distri-butions for Rh ¼ 80%. Note that the standard devia-tion and modal radius values for the fine and coarsemodes, respectively, are larger and smaller thanvalues shown in Fig. 5(a).

To ensure that our models exhibit the same spec-tral dependence of SSA as observed in Fig. 3(c), weperformed the Mie calculations for all the wave-lengths of the SeaWiFS sensors, and computed theeffective radius and SSA values for the 80 models(8Rh × 10 fine-mode fraction) described above. Next,we interpolated these values for the relative humid-ity and effective radius values of the CBR aerosols

Fig. 4. (a) Growth of fine- and coarse-mode aerosol radius with an increase inRh over the open ocean. The symbols represent themonthlymean radius data and the solid and dashed curves represent the model results (Hänel [13]). (b) Same as (a), except for CBR. (c) Change inthe standard deviation of fine- and coarse-mode distributions with Rh over the open ocean. The symbols represent the monthly meanstandard deviation values and the solid and dashed curves are the least square fit to the data. (d) Same as (c), except for CBR.

Table 3. Complex Refractive Index Values for Different Constituents of the Fine- and Coarse-Mode Aerosols for SeaWiFS Sensorat Rh ¼ 0ðSF79Þ

Wavelength (nm) Water Soluble Dustlike Sea Salt Soot Water

412 1:530 − 3:0050i 1:530 − 3:0080i 1:500 − 3:0000i 1:750 − 3:4586i 1:338 − 3:0000i443 1:530 − 3:0050i 1:530 − 3:0080i 1:500 − 3:0000i 1:750 − 3:4551i 1:337 − 3:0000i490 1:530 − 3:0050i 1:530 − 3:0080i 1:500 − 3:0000i 1:750 − 3:4500i 1:335 − 3:0000i510 1:530 − 3:0050i 1:530 − 3:0080i 1:500 − 3:0000i 1:750 − 3:4500i 1:334 − 3:0000i555 1:530 − 3:0060i 1:530 − 3:0080i 1:499 − 3:0000i 1:750 − 3:4394i 1:333 − 3:0000i670 1:530 − 3:0066i 1:530 − 3:0080i 1:490 − 3:0000i 1:750 − 3:4300i 1:331 − 3:0000i765 1:526 − 3:0091i 1:526 − 3:0080i 1:486 − 3:0000i 1:750 − 3:4300i 1:330 − 3:0000i865 1:520 − 3:0121i 1:520 − 3:0080i 1:480 − 3:0000i 1:750 − 3:4303i 1:329 − 3:0000i


described in Fig. 3(c). An example of the comparisonfor the month of September is shown in Fig. 6(a).What we find is that our predicted SSA between700 and 900nm drops off much faster than that ob-served in the AERONET data. The results for othermonths were similar. We attribute the sharp drop incalculated SSA to an increase in the value of theimaginary part of the refractive index of the water-soluble aerosols that constituted 70% of the fine-mode aerosols. We also noted that the real part ofrefractive index for water-soluble and dustlike aero-sols were essentially the same in the visible andnear-IR part of the spectrum. Also, in the same partof the spectrum, the imaginary part of the dustlikeaerosols were almost constant and were a little high-er than for water-soluble aerosols. Based on theseobservations, we varied the composition of the fine-mode aerosols and found that a mixture of 99.5% ofdustlike aerosols and 0.5% of soot gave a reasonablygood agreement with the AERONET data. An exam-ple for the month of September is shown in Fig. 6(b).Results for other months were very similar, exceptfor the month of October, where the predicted valuesof SSA at all wavelengths were lower by ∼1%.

4. Impact of New Models on Satellite Ocean Color andAerosol Retrievals

To evaluate the impact of the aerosol model changeson satellite sensor retrievals of aerosol optical thick-ness, τ, and water-leaving radiance, Lw, we incorpo-rated the new models into the operational version ofNASA’s ocean color processing code, 12 gen. The op-erational code uses the GW94 algorithm to deter-

mine the aerosol contributions, and it employs aniterative bio-optical model (Bailey et al. [30]) to sepa-rate the aerosol and water signals in complex turbidwaters. Implementation of the new models withinthe NASA code was achieved through generationof a new set of LUTs to replace the standard SF79LUTs. The new LUTs were created with the currentversion of Ahmad and Fraser’s vector radiativetransfer code [31] for the ocean–atmosphere system.

Althoughwe did not change the operational proces-singalgorithmofGW94,useof thenewtablesrequiredthat we assign an Rh value to each instantaneousfield of view (IFOV). The concept is to select two Rhvalues from the LUTs that bracket the IFOV valueand, for each Rh value, use its ten aerosol models tocompute aerosol reflectance (ρaλ) at all wavelengths(λ), and then use the weighted sum to determine thebest estimates of aerosol reflectance.

Initial processing of the SeaWiFS data showed asignificant frequency of cases where scaled reflec-tance ϵ765ð¼ ρa765=ρa865Þ, as determined from the sa-tellite data, was below the range of values in theLUTs. This suggested that the sensor was sometimesobserving aerosol size distributions with larger par-ticles than the mean observations measured at theopen-ocean AERONET sites. To ensure that the mod-el size distributions spanned the full range of thesatellite observations, we decided to increase theoceanic coarse-mode radius (rvc) by 3σ, where σ isthe standard deviation of the monthly mean of thecoarse-mode AERONET oceanic data. This allowedthe models ϵ765 values to span the range of observedϵ765. The revised values of rvc are given in Table 4.

Fig. 5. (a) Examples of the new size distributions (Rh80M02 and Rh80M05). Both distributions are normalized to a value of 100 at theirrespective maxima. (b) Examples of two SF79 aerosol size distributions. C50 and C80 refer to coastal aerosol distributions for Rh of 50%and 80%, respectively.

Table 4. Modal Radii ðrvf ; rvc Þ, Standard Deviations ðσf ; σc Þ, and Ratios of Wet-to-Dry Aerosol Radius ðrvf =rovf ; rvc=rovc Þ for Eight Valuesof Relative Humidity Used in This Studya

Rh rvf σf rvc σc rvf =rovf rvc=rovc

0.30 0.150 0.437 2.441 0.672 1.006 1.0090.50 0.152 0.437 2.477 0.672 1.019 1.0240.70 0.158 0.437 2.927 0.672 1.063 1.2100.75 0.167 0.437 3.481 0.672 1.118 1.4390.80 0.187 0.437 3.966 0.672 1.255 1.6390.85 0.204 0.437 4.243 0.672 1.371 1.7530.90 0.221 0.437 4.638 0.672 1.486 1.9170.95 0.246 0.437 5.549 0.672 1.648 2.293

aThe subscripts v, f , and c, respectively, refer to volume space, fine mode, and coarse mode of the aerosols


Using the aerosol model LUTs derived fromTable 4, we processed a subset of the SeaWiFS mis-sion consisting of full global area coverage for everyeighth 4-day period spanning the period from late1997 through 2009. To further isolate the effect ofaerosol model change and associated Rh-based mod-el selection, we also updated the vicarious calibrationusing the standard approach outlined in Franz et al.[32]. This has the effect of altering the 765nm cali-bration to force the mean angstrom coefficient retrie-val at the South Pacific Gyre (SPG) to be the same forboth the old and newmodel suites. The water-leavingradiances were then recalibrated against the MOBYin-water buoy using the vicariously calibrated aero-sol reflectance retrievals.

The results of this processing test are shown inFigs. 7(a) and 7(b), where results are plotted as afunction of time for all data collected over deep-ocean

water (depth greater than 1000m). Figure 7(a) showsthat τ865 values retrieved from the new models arelower than those retrieved from old models. The mis-sion-average value of τ865 retrieved over deep oceanfrom the new aerosol models is 0:100� 0:004, whichis close to the average AERONET value for τ870 of0:086� 0:066, for the eight open-ocean sites usedin this study. The average value of τ865 retrievedusing the old models is 0:131� 0:005. Figure 7(b)shows a temporal trend comparison of Lwn for the412, 490, and 555nm bands of SeaWiFS, averagedover all deep-water retrievals. Note that Lwn is sim-ply equal to LwðF0=EdÞ, where Fo and Ed are, respec-tively, the solar irradiance at the top and bottom ofthe atmosphere. The results show that the retrievedLwn values from the two sets of aerosol models (oldand new) over the same region of the deep oceanare essentially the same. In the blue bands at 412

Fig. 7. (a) Ten-year time series of τ865 over deep ocean derived from SeaWiFS sensor using new and old aerosol models. (b) Ten-year timeseries of normalized water-leaving radiances, Lwn, over deep ocean derived from SeaWiFS sensors using new and old aerosol models. (c)TOA reflectance computed from old (M70) and new (Rh80M06) aerosol models. The input parameters were θ0 ¼ 30°, θ ¼ 42°, ϕ ¼ 120°, andτ ¼ 0:1 (d) Same as (c), except that the reflectances for each aerosol model were normalized by their respective value for the 865nm band.

Fig. 6. (a) Comparison of spectral dependence of SSA as reported by AERONET for τ870 ≤ 0:3, and as predicted by our model where thefine mode consists of 70% water-soluble and 30% dustlike aerosols. (b) Same as in (a), except the fine mode consists of 99.5% dustlikeaerosols and 0.5% soot aerosols.


and 490nm, the new (old) values of Lwn are, respec-tively, 1:744� 0:056 and 1:557� 0:041 (1:750�0:056 and 1:566� 0:041) mW=cm2=Sr=μm, and inthe green band at 555nm, the value is 0:338�0:008 ð0:342� 0:007ÞmW=cm2=Sr=μm.

The results in Fig. 7(a) can be explained. We knowthat, at small aerosol optical thickness values, thesingle scattering phenomenon dominates the scatter-ing process and, aside from constant terms involvingsolar irradiance and the cosine of solar and sensorview angles, the aerosol reflectance is essentially aproduct of SSA (ωo), phase function (p), and aerosoloptical thickness (τ). If we look at Figs. 5(a) and 5(b),we find that the size distributions of the old modelsare broad and contain more large particles than thenew distributions. Since large particles have smallvalues of phase function in the backward direction,the old models will retrieve a larger value of opticalthickness than the new models, and this is what wesee in Fig. 7(a).

The results in Fig. 7(b) are more intriguing. Inspite of large differences in aerosol optical thickness[see Fig. 7(a)], the differences in water-leaving ra-diances are very small (�1% for the 412 and 490nmbands and �3% for 555nm). This result is, in part,due to the vicarious calibration, which forces the re-trieved water-leaving radiances near Lanai, Hawaiito agree, on average, with the MOBY in situ radio-metric buoy (Franz et al. [32]). To understand the re-sults in Fig. 7(b) further, we again consider the singlescattering formalism. Here, the most importantthing to recognize is that the aerosol reflectance,and, thus, the atmospheric correction, does not de-pend on the spectral dependence of individual para-meters (τ, p, and ωo), but on the spectral dependenceof the product of parameters τ, p, and ωo, which,apart from a constant, is the same as reflectance.In other words, two aerosol models with different va-lues of τ, p, and ωo, and, hence, different reflectancevalues, can have very similar spectral dependence.We show an example of this in Fig. 7(c), where thetwo curves show the spectral dependence of TOA re-flectance for two aerosol models, M70 (old model) andRh80M06 (new model). If we compute the reflectancefor an aerosol optical thickness of 0.1, we will findthat the two models yield completely different va-lues, yet these values show very similar spectral de-pendence. In fact, if we scale the reflectance valuesfor the two models by their respective values at865nm, the resulting curves are nearly identical.This is shown in Fig. 7(d). At present it is difficultto say under what conditions two aerosol modelswould show similar spectral dependence, but indica-tions are that, if the aerosols are nonabsorbing orweakly absorbing and have very similar angstromcoefficients and ϵ765 values, then they will show verysimilar spectral dependence.

We emphasize again that this initial test was de-signed to yield similar angstrom coefficients at theSPG for both the old and new models, due to themethod employed to vicariously calibrate the satel-

lite retrievals (Franz et al. [32]). Specifically, we tar-geted the calibration in the SPG to yield α510 ¼ 0:2,which was based on the idea that aerosols over theSPG are predominately maritime in origin, andthe old SF79 maritime model at 90% humidity pro-vided an angstrom of 0.2. Given that the new aerosolmodels are designed to match AERONET size distri-butions, it is now appropriate to change the vicariouscalibration to directly target AERONET retrievals.The vicarious calibration for SeaWiFS was, there-fore, revised to match the mean angstrom coefficientobserved at the Tahiti AERONET site (nearest to theSPG), which is approximately α440 ¼ 0:68. Relative tothe initial processing results using the new models,this change in calibration, followed by an associatedrecalibration of the visible bands to MOBY, again re-sulted in only a minor change to the water-leavingradiance retrievals (2%–3% decrease) over deep-ocean waters. The mean deep-water α510, however,increased from 0.3 to 0.7, while the τ865 retrievalsdecreased by only 4%.

5. Application to Ocean Color Reprocessing andAssessment of Results

The new aerosol models and Rh-based model selec-tion scheme were incorporated into NASA’s opera-tional ocean color processing code in preparation forSeaWiFS reprocessing. This update included the re-vised vicarious calibration based on the AERONETmeasurements at Tahiti, as well as a host of otherchanges to the processing algorithms that are beyondthe scope of this manuscript, but which have little ef-fect on the aerosol retrievals. Here, we compare thereprocessing results for τ865 and α443 with AERONETmeasurements of τ870 and α440 over two sites: Bermu-da andChesapeakeBay (Wallops Island) that, respec-tively, represent open-ocean and coastal waters. Tominimize the large statistical fluctuations in the indi-vidual match-up values, we utilized the monthlymean values of τ and α for comparison. This approachallowsus touseall available retrievals for the compar-ison, and better reveal the true aerosol properties.

To create the match-up database, a box of �0:25degrees in latitude and longitude was constructedaround the AERONET site while ensuring that theentire box was over the ocean. For the satellite,1km resolution (MLAC) Level 2 daily SeaWiFS datawere selected and quality screened following the pro-tocols in Bailey and Werdell [33]. For the AERONETdata, the Level 2 daily averaged products of directSun measurements were used. The Level 2 productsatisfies all the quality control criteria, includingthin clouds in the field of view.

The results on the comparison of optical thicknessoverBermudaandWallopsIslandfortheperiodshowninTable1are,respectively,showninFigs.8(a)and8(b).The numbers of matchups are 53 and 94. The solidline is the 1∶1 line and the dashed lines representthe �0:02 uncertainty in the retrieved optical thick-ness. The uncertainty of�0:02 is considered a desiredgoal of retrieving aerosol optical thickness from


satellite measurements (Mishchenko et al. [34]). Wefind the agreement between the satellite retrievalsof τ865 andAERONETmeasurementsof τ870 tobegood,with81%ofthedataoverBermudaand78%ofthedataover Wallops Island falling within the desired uncer-tainty of �0:02. The bias and rms error statistics forBermuda (Wallops Island) are, respectively, 0.010(−0:009) and0.002 (0.002).Timeseriesof optical thick-ness over the two sites, for both SeaWiFS (using thenew aerosol models) and AERONET are shown inFigs. 8(c) and 8(d). For comparison purposes, we alsoshow the time series for SeaWiFS as determined fromthe old aerosol models. It is apparent that the opticalthicknessesderivedfromthenewaerosolmodelsareinbetter agreement with the AERONET observationsthan those obtained from the old models. Although

the oldmodels do show the same trend, themagnitudeof retrieved optical thickness is higher than that ob-served in theAERONETdata.This observation is con-sistentwith the conclusions ofWang et al. [15] that theSF79 models overestimate the aerosol optical thick-ness over the ocean. It is interesting to note that, overWallops Island, the newmodels faithfully capture themagnitude as well as the trend in optical thickness.

We also compared the α443 retrieved from SeaWiFSusing the new models with α440 from AERONET. Atime series of angstrom coefficient for each site isshown in Figs. 8(e) and 8(f). For comparison pur-poses, we also show the time series of α443 retrievedfrom the old models. Again, we find that the resultsfrom the new aerosol models are in very good agree-ment with AERONET. The average value of α443 from

Fig. 8. (a) Scatter plot of SeaWiFS versus AERONET monthly mean aerosol optical thickness (τ) over Bermuda. The solid curve is a 1∶1curve and the dotted curves represent �0:02 change in τ from the 1∶1 curve. Approximately 81% of the data are within the dotted curves.The robust least squares fit equation is τSeaWiFS ¼ 0:860τAERONET þ 0:015, and bias and rms statistics are, respectively, 0.010 and 0.002. (b)Same as in (a), except that 78% of the data are within the dotted curves. The robust least squares fit equation isτSeaWiFS ¼ 0:944τAERONET − 0:005, and the bias and rms statistics are, respectively, −0:009 and 0.002. (c) Time series of monthly meanaerosol optical thickness (τ865) over Bermuda derived from the old and the new models as well as from AERONET sunphotometer. Notethat τ values derived from the new models are much closer to AERONET than those derived from the old models. (d) Same as (c) , exceptthat the data were taken over Wallops Island. (e) Time series of monthly mean angstrom coefficient (α443) over Bermuda derived from theold and the newmodels as well as from the AERONET sunphotometer. Note that α values derived from the new models are much closer toAERONET than those derived from the old models. (f) Same as (e), except that the data were taken over Wallops Island. The AERONETvalues are slightly larger than those retrieved from the new models.


the newmodels is 0:841� 0:171 and fromAERONETis 0:891� 0:211. The average value of α443 from theold models is 0:394� 0:087, which is significantlylower than AERONET value.

6. Summary and Conclusions

In this paper, we have described the development of anew suite of aerosol models to reduce the satellitedata from the SeaWiFS and MODIS sensors andretrieve aerosol optical thickness (τ), angstrom coef-ficient (α), and the water-leaving radiances (Lw)originating from the sub-surface of the ocean. Thelatter is needed to quantify phytoplankton chloro-phyll-a, CDOM, and primary productivity of theocean. There was an urgent need for new aerosolmodels because the old models used by the OBPG un-til recently were based on SF79 models that were de-veloped for climate and radiation studies and it wasfound that, over the ocean, the old models consis-tently overestimated τ and underestimated α.

To develop the suite of new aerosol models, we con-sidered a number of oceanic and coastal AERONETsites and selected eight sites over open ocean andthree sites over the CBR.We used the CBR as a proxyfor the coastal waters because it is highly turbid inthe north and nearly oceanic in the south, and aero-sols over this region are influenced by industrial andcity pollutions, agricultural land use, and the Atlan-tic Ocean. We analyzed the open-ocean and CBR dataseparately. To get a better understanding of the var-iation in aerosol microphysical and optical proper-ties, we converted the daily averaged data intomonthly averages and examined in detail the seaso-nal behavior of a few selected parameters, includingmean geometric modal radius (in dV=dðln rÞ space),standard deviations, effective radius, and relativeconcentration of fine- and coarse-mode particles. Wefound that, over the CBR, both the fine- and coarse-mode particle size distributions showed a strong sea-sonal dependence, with maximum modal values inthe summer time; however, the standard deviationvalues were relatively constant. Over the open-ocean, modal radii showed a weak seasonal depen-dence and the standard deviation values were noisyand did not show any seasonal dependence.

We also found that the seasonal variability of themodal radii (r) of the fine- and coarse-mode aerosolswas correlated withRh, and that this correlation wasconsistent with Hänel’s model [13] of growth of par-ticle radius with Rh.

Using AERONET retrievals as a guide, we con-structed a set of bimodal lognormal aerosol size dis-tributions, where the modal radius and refractiveindex values were explicitly dependent on Rh. Forstandard deviation, we decided to use the average va-lue of all the monthly means. The rationale was that,although there was a trend in the data, there was noguiding physics to extend the trend outside thehumidity range of the observations.

After defining the details of the modal radii, stan-dard deviations, and refractive indices of the fine and

coarse modes, we constructed ten distributions (foreach relative humidity value) by varying the fine-mode fraction from zero to 1. In all, we created 80distributions (8Rh × 10 fine-mode fraction) to processthe satellite data. Also, to ensure that our new mod-els exhibited the same spectral dependence of SSA asobserved in the AERONET data, we varied the com-position of the fine-mode aerosols and found that amixture of 99.5% of dustlike aerosols and 0.5% of sootgave a reasonably good agreement (approximately�1%) with the AERONET data.

Initially,we processed a subset of the SeaWiFSmis-sion data using both the new and old aerosol modelsand retrieved aerosol optical thickness, τ, angstromcoefficient, α, and water-leaving radiance, Lw, overthe ocean. We found that the average τ865 value overdeep ocean using the new aerosol models was0:100� 0:004, whereas the average τ870 value fromAERONET for the eight open-ocean sites used in thisstudywas 0:086� 0:066. The τ865 value from oldmod-elswas0:131� 0:005, whichwas substantially higherthan the AERONET value. In contrast, the retrievednormalized water-leaving radiance, Lwn, from thenew and the old sets of aerosol models over the deepocean changed by only a few percent. In the blue bandat 412nm, the new (old) values of Lwn were 1:744�0:056 (1:750� 0:056 ) mW=cm2=Sr=μm, and in thegreenbandat555nm, thenew (old) values ofLwnwere0:338� 0:008 (0:342� 0:007) mW=cm2=Sr=μm.

The fact that the τ865 retrieved values from the newmodels are smaller than from the old models can beeasily explained by noting that the old aerosol mod-els are broad (large standard deviation) and havemore large particles in them than the new models.Since large particles scatter less in the backward di-rection, the old models having smaller values ofphase function (p) in the backward direction wouldyield larger values of aerosol optical thickness thanthe new models.

Also, we believe that the changes in the Lwn aresmall partly due to the approach employed forvicariously calibrating the water-leaving radiance re-trievals, and because the new and oldmodels can pro-duce very similar spectral dependence. This can befurther explained in the following way. We know thatfor a given set of radiance measurements, the inver-sion theory (i.e., retrieval of size distribution from aset of radiance measurements) does not guaranteea unique solution; rather, it admits many solutions.Therefore, it is not surprising that two sets of aerosoldistributions would yield the same atmospheric cor-rection and, hence, the same values of Lwn. In addi-tion, the most important thing to recognize is thatthe atmospheric correction does not depend on thespectral dependence of individual parameters (τ, p,and ωo), but rather depends on the spectral depen-dence of scaled reflectance ϵλð¼ ρaλ=ρa865Þ. In otherwords, two aerosol size distributions with differentmodal radii and standard deviations can have very si-milar spectral dependence of ϵλ and, hence, very simi-lar atmospheric correction. An example of this is


shown in Fig. 7(d). At present it is difficult to say un-der what conditions two aerosol models would showsimilar spectral dependence. However, it appearsthat, if the aerosols are nonabsorbing or weakly ab-sorbing and have very similar angstrom coefficientsand very close ϵ765ð¼ ρa765 − ρa865Þ values, that is,the reflectances have the same spectral trend over765 to 865nm, then they will most likely show verysimilar spectral dependence and, hence, similar at-mospheric correction.

As a part of error analysis, we found that the re-flectance measurements in the 765 and 865 bandsof SeaWiFS essentially define the coarse mode of thedistribution, whereas, the ϵ765 value, which is the ra-tio of ρa765=ρa865, locks the relative weights of the fineand coarse modes. Hence, the error in reflectance va-lues, ρaλ, at a shorter wavelength (blue or green partof the spectrum) would depend on the modal radius(rvf ) and standard deviation (σf ) of the fine mode. Inreality, any change in the values of these two para-meters will also affect the computed ϵ765. The mag-nitude would depend on the sensitivity of ϵ765 on rvfand σf .

Finally, we showed the aerosol optical thicknessand angstrom coefficients retrieved for SeaWiFSusing the new aerosol models and the revised vicar-ious calibration are now in very good agreement withAERONET measurements. We demonstrated that81% of SeaWiFS τ865 retrievals over Bermuda and78% of the τ865 retrievals over Wallops Island agreewith AERONET to within an uncertainty of �0:02.The average value of α443 from the new models overBermuda is 0:841� 0:171, which is in good agree-ment with the AERONET α440 value of 0:891�0:211. The average value of α443 from the old modelswas 0:394� 0:087, which is significantly lower thanthe AERONET value.

We would like to thank Bo-Cai Gao of the NavalResearch Laboratory (NRL) and Suraiya P. Ahmadof INNOVIM for many useful discussions and sug-gestions, and the members of OBPG, in particular,W. D. Robinson, for providing meteorological datafor the analysis of AERONET observations. Also,we thank AERONET staff for maintaining and pro-viding the sunphotometer data used in this study. Inaddition, we would like to thank two anonymous re-viewers for their helpful comments. Eric P. Shettle’swork was supported by a grant from NASA’s Office ofEarth Science and by NRL internal funding [from theOffice of Naval Research (ONR)].

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